We previously proposed a Sub-path Enumeration and Pruning (SEP) approach [8]

1
Discovering Interesting Sub-paths in
Spatiotemporal Datasets
Xun Zhou1, Shashi Shekhar1, Stefan Liess2, Peter
K. Snyder2, Pradeep Mohan1 1 Department of
Computer Science and Engineering, 2Department of
Soil, Water and Climate, University of Minnesota
xun, shekhar, mohan_at_cs.umn.edu, liess,
pksnyder_at_umn.edu
1. Motivation
4. Approach
6. Computational Speedup

• The Sahel region in Africa is prone to severe
  drought due to climate change
• What is unique about the Sahel?
• Narrow transitional zone between rainforest and
  desert (ecotone)
• Environmental attributes (e.g., vegetation cover)
  change sharply
• Vulnerable to climate change

• We previously proposed a Sub-path Enumeration and
  Pruning (SEP) approach 8
• Sub-path interestingness is measured by Sameness
  Degree (an algebraic aggregate function of
  slopes)
• Compute piecewise slope, flag top and bottom a
  percentile segments as abrupt units (user given
  a).
• Sameness degree (SD) ranging 0, 1 is a function
  of piecewise slopes in a sub-path
• Define a test of the pattern SD?(given
  threshold)
• Enumerate all the intervals in the data and test
  with the above criterion using SEP .
• Decompose the statistical function into simple
  functions (e.g., SUM, COUNT) and pre-compute.
• Row-wise strategy For each end unit, examine
  longer intervals first. Need further pruning.
• Top-down strategy For all the intervals, always
  examine longer ones before its subsets.
• We further proposed a SEP with Pruning Border
  (SEPPER) approach that further optimize the
  enumeration
• The strategy combines linear (row-wise) and
  top-down searching strategy
• Space-time complexity superior to both SEP
  row-wise and top-down approaches
• SEPPERs Time complexity MinSEP top-down, SEP
  row-wise
• SEPPERs Space complexity MinSEP top-down, SEP
  row-wise

• Experiment Setup
• Climate model forecast time series (WCRP-CHFP IRI
  ECHAM4p5-MOM3-DC2fmt2 ATM)
• Synthetic data sequences with piecewise slope
  generated using Gaussian distribution
• Variables
• Pattern Length Ratio (PLR) ratio of interesting
  interval length against data length
• Data length

Vegetation cover of Africa from the GIMMS NDVI
dataset 6

• Are there other regions that share similar
  features in the world?
• Help understand and predict possible severe
  climate impacts
• Find spatial intervals of abrupt changes

Vegetation cover (in NDVI) along 18.5E longitude

• Alternative example a similar pattern can be
  found in time series
• Rapid increase/decrease of precipitation/temperat
  ure in a few years
• Help identify events such as droughts from
  historical data.

5. Case Study Interesting Sub-path with Abrupt
Change
1. Case study on Africa vegetation cover (NDVI)
dataset6

• Major spatial abrupt changes (ecotones) found
  the Sahel and the southern boundary of tropical
  rainforest
• Other ecotones with abrupt changes in vegetation
  cover in the world the Gobi Desert (Asia),
  Western America, etc
• Hypothesis these areas may also be vulnerable to
  Sahel-like eco-changes.

7. Conclusions
Vegetation cover in Africa, August 1-15, 1981.
Abrupt vegetation cover change in Africa, August
1-15, 1981.

• We developed a data mining approach named SEP to
  find intervals of abrupt change in eco-climate
  data. Case studies on real datasets show that
  the proposed approach can discover major spatial
  and temporal intervals of abrupt change.
• Further, we developed the SEPPER approach which
  improved the computational efficiency over SEP.
  Experimental evaluation verified the tradeoff
  between the two previous SEP design decisions and
  show dominance of the new SEPPER algorithm over
  them.

Precipitation time series in the some region in
Africa
Source 1.Sahel rainfall index data, Joint
Institute for the Study of the Atmosphere and
Ocean (JISAO). http//jisao.washington.edu/data/sa
hel/ 2. Foley et al, Regime Shifts in the Sahara
and Sahel Interactions between Ecological and
Climatic Systems in Northern Africa. Ecosystems
(2003) 6 524539
2. Challenges

• The length of the change intervals vary
• The interestingness of the sub-path may not
  exhibit monotonicity (e.g., a long decreasing
  interval may contain a short increasing part)
• The data volume can be very large.

Vegetation cover map (in NDVI) of
Africa (left), abrupt change of vegetation cover
in Africa in August 1981 (middle), and global
analysis for the same period (right)
8. Acknowledgements and References
2. Case study on Sahel rainfall index data7

• Major temporal abrupt changes found by the
  proposed approach
• Decreasing period in late 1960s and mid 1980s2.
• Long decrease (1950-1980)3 found when using
  larger abruptness percentile parameter.
• We found long periods of persistently high/low
  precipitation using a slightly modified interest
  measure.

3. Novelty

• Support for this research was provided by the
  following grants
• National Science Foundation under Grant No.
  1029711, III-CXT IIS-0713214, IGERT DGE-0504195,
  CRIIAD CNS-0708604, USDOD under Grant No.
  HM1582-08-1-0017, HM1582-07-1-2035, and
  W9132V-09-C-0009.
• 1 D. Nikovski and A. Jain. Fast adaptive
  algorithms for abrupt change detection. Machine
  learning, 79(3)283-306, 2010.
• 2 G. Narisma, J. Foley, R. Licker, and N.
  Ramankutty. Abrupt changes in rainfall during the
  twentieth century. Geophysical Research Letters,
  34(6)L06710, 2007.
• 3 A. Dai, P. Lamb, K. Trenberth, M. Hulme,
  P. Jones, and P. Xie. The recent sahel drought is
  real. International Journal of Climatology,
  24(11)1323-1331, 2004.
• 4 I. Noble. A model of the responses of
  ecotones to climate change. Ecological
  Applications, 3(3)396-403, 1993.
• 5 E. Page. Continuous inspection schemes.
  Biometrika, 41(1/2)100-115, 1954.
• 6 Tucker, C.J., J.E. Pinzon, M.E. Brown.
  Global inventory modeling and mapping studies.
  Global Land Cover Facility, University of
  Maryland, College Park, Maryland, 1981-2006.
• 7 Joint Institute for the Study of the
  Atmosphere and Ocean(JISAO). Sahel rainfall
  index. http//jisao.washington.edu/data/sa
  hel/.
• 8 Xun Zhou et al, Discovering Interesting
  Sub-paths in Spatiotemporal Datasets A Summary
  of Results. In Proc. ACM SIGSPATIAL GIS (GIS11)
  pp 44-53. Chicago, IL, USA, 2011.

• Related statistical methods (e.g., CUSUM1, 5)
  only find collections of interesting
  time-points/spatial locations (e.g., with abrupt
  changes), rather than long intervals of change.
• Some other work in climate research 2 are not
  completely automated.

Upper Smoothed yearly Sahel rainfall index.
Lower (left) abrupt precipitation change found
when using a0.25 and ?0.5. (center) abrupt
precipitation change found when using a0.25 and
?0.3, (right) persistent high/low precipitation
periods.
Abrupt change in a sample data sequence found by
CUSUM5 (left figure, location 6) and our work
(right figure, interval 5-11)
Location in the data sequence
Location in the data sequence